Fórum de Matemática
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Amigos, como simplifico

\(( 2^-^{\frac{2}{3}} -3^-^{\frac{2}{3}}). (\sqrt[3]{3} - \sqrt[3]{2})^{-1}. \sqrt[3]{36}\)



Resposta: \(2^{ \frac{1}{3}}+ 3^{ \frac{1}{3}}\)

\(\frac{6^{2/3}(2^{-2/3}-3^{-2/3})}{3^{1/3}-2^{1/3}}=\frac{(2.3)^{2/3}(2^{-2/3}-3^{-2/3})}{3^{1/3}-2^{1/3}}=\frac{(2^{2/3}.3^{2/3})(2^{-2/3}-3^{-2/3})}{3^{1/3}-2^{1/3}}\)


\(=\frac{(3^{2/3}-2^{2/3})}{3^{1/3}-2^{1/3}}=\frac{((3^{1/3})-(2^{1/3}))((3^{1/3})+(2^{1/3}))}{3^{1/3}-2^{1/3}}=3^{1/3}+2^{1/3}\)